FHA is only for primary residences and you can't currently own a home or have owned one within the last 5 years (first time homebuyer) - THIS IS NOT TRUE.
You're in a tough spot. If your current home has an FHA loan you will not be able to buy another home using an FHA loan unless you qualify for one of the few exceptions like you moved out of the area for work.
Your credit score needs to be at least 620+ to qualify for FHA, VA or USDA but a conventional will require either 20% down or a much higher credit score (680+)
The biggest issue is the multiple mortgage lates in the last 12 months. You say you can handle 2 separate mortgages but a lender is going to look at your payment history and say you can't afford to pay the one you've got.
You're best bet is to start off by disputing your mortgage lates to see if you can get them deleted.
Please see my blog with tips and advice on shortsales
You have two problems here: 1) FHA will not approve you if you already own a home; and 2) You say you have more than 2 late payments, which will make it hard to even qualify for a conventional mortgage (as per Freddie and Fannie guidelines).
I'm trying to understand your situation here. How are you late on payments and claiming that you can afford a second? Now by late payment do you mean a few days late (but you pay with late fee) or do you mean more than 30 days late, which leads to a ding on your credit report. If you answered more than 30 days late, then no lender will want to approve that loan.
FHA is only for primary residences and you can't currently own a home or have owned one within the last 5 years (first time homebuyer).
The third problem you'd face is FHA guidelines. 620 is the minimum score, provided you meet all other eligibility criteria.
NACA (a non profit) is a great organization for those backed up on mortgages or looking to purchase properties (first time homebuyers only). Go to NACA.com for more info.
Unfortuantely, if you're home has been on the market for a year and hasnt sold, its likely due to pricing. Has your agent given you an honest opinion of value?
Visit makinghomeaffordable.gov to see where you can go for free help on obtaining a loan modification if you're having trouble with your current mortgage.